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Some exponential Diophantine equations. (English) Zbl 1221.11089
The author studies the diophantine equations $$x^x=y^y$$, $$x_1^{x_1}x_2^{x_2}=y_1^{y_1} y_2^{y_2}$$ and $$x_1^{x_1}x_2^{x_2}x_3^{x_3}=y_1^{y_1} y_2^{y_2}y_3^{y_3}$$.
##### MSC:
 11D61 Exponential Diophantine equations
##### Keywords:
exponential Diophantine equations